This is a summary of the primary figures and tests I have completed for Chapter 2 as of my oral exams (April 2018), as well as accompanying notes and questions.

1 Correlations among predictor variables

1.1 Benthic variables

1.2 Selected fish and benthic variables

2 PCAs

2.1 All predictors

predictors <- site.sum %>% select(cover_LC,cover_TA,canopy_MA,canopy_TA,rugosity,scar.BM,scar.DEN,carn.BM) # should it matter if I use site level summary data vs. full follow dataset (where site-level data has been joined?)
pca <- prcomp(na.omit(predictors),center = TRUE,scale. = TRUE) 
summary(pca)
## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6
## Standard deviation     2.1310 1.4982 0.79477 0.47902 0.45634 0.30914
## Proportion of Variance 0.5677 0.2806 0.07896 0.02868 0.02603 0.01195
## Cumulative Proportion  0.5677 0.8482 0.92719 0.95587 0.98190 0.99385
##                            PC7     PC8
## Standard deviation     0.21046 0.07020
## Proportion of Variance 0.00554 0.00062
## Cumulative Proportion  0.99938 1.00000
plot(pca,type="l")

ggbiplot(pca, obs.scale = 1, var.scale = 1, groups=site.sum$Island, ellipse = TRUE, circle = TRUE, varname.size = 2) + scale_color_manual(name="Island", values=c("navy", "darkseagreen", "slategray2")) + theme(legend.direction = 'horizontal', legend.position = 'top') + theme_minimal()

2.2 Benthic predictors

3 Grazing differences between islands

3.1 Feeding rates

##             Df   Sum Sq Mean Sq F value   Pr(>F)    
## Island       2 19315250 9657625   24.65 2.57e-09 ***
## Residuals   93 36432745  391750                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = FR ~ Island, data = vet20init)
## 
## $Island
##                      diff       lwr       upr     p adj
## Barbuda-Antigua -42.79233 -540.4860  454.9014 0.9771505
## Bonaire-Antigua 903.54977  493.9521 1313.1474 0.0000028
## Bonaire-Barbuda 946.34211  553.9021 1338.7821 0.0000003

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2   0.117 0.8897
##       93
##              Df  Sum Sq Mean Sq F value   Pr(>F)    
## Island        2 3765399 1882699   25.35 5.73e-10 ***
## Residuals   125 9283349   74267                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = FR ~ Island, data = vir20init, white.adjust = TRUE)
## 
## $Island
##                      diff       lwr      upr     p adj
## Barbuda-Antigua 315.65455  164.6361 466.6730 0.0000068
## Bonaire-Antigua 364.50714  234.9929 494.0214 0.0000000
## Bonaire-Barbuda  48.85258 -105.4620 203.1672 0.7336418

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   2  2.2444 0.1102
##       125

3.2 Bite rates

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Island       2  0.519  0.2594   2.501 0.0875 .
## Residuals   93  9.646  0.1037                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = BR ~ Island, data = vet20init, white.adjust = TRUE)
## 
## $Island
##                       diff         lwr       upr     p adj
## Barbuda-Antigua 0.08541907 -0.17066607 0.3415042 0.7073489
## Bonaire-Antigua 0.18703474 -0.02372113 0.3977906 0.0925502
## Bonaire-Barbuda 0.10161566 -0.10031186 0.3035432 0.4570074

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value    Pr(>F)    
## group  2  9.2302 0.0002205 ***
##       93                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##              Df Sum Sq Mean Sq F value Pr(>F)
## Island        2  0.018 0.00881   0.176  0.839
## Residuals   125  6.248 0.04998
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = BR ~ Island, data = vet20init, white.adjust = TRUE)
## 
## $Island
##                       diff         lwr       upr     p adj
## Barbuda-Antigua 0.08541907 -0.17066607 0.3415042 0.7073489
## Bonaire-Antigua 0.18703474 -0.02372113 0.3977906 0.0925502
## Bonaire-Barbuda 0.10161566 -0.10031186 0.3035432 0.4570074

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)    
## group   2  10.278 7.37e-05 ***
##       125                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

3.3 Fraction of time spent grazing

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Island       2  0.519  0.2594   2.501 0.0875 .
## Residuals   93  9.646  0.1037                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value    Pr(>F)    
## group  2  9.2302 0.0002205 ***
##       93                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##              Df Sum Sq Mean Sq F value Pr(>F)
## Island        2  0.018 0.00881   0.176  0.839
## Residuals   125  6.248 0.04998

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)    
## group   2  10.278 7.37e-05 ***
##       125                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

3.4 Grazing intensity

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## Island       2   1454   727.2   8.178 0.000553 ***
## Residuals   88   7826    88.9                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 5 observations deleted due to missingness
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = for.bites ~ Island, data = vet20init, white.adjust = TRUE)
## 
## $Island
##                      diff       lwr       upr     p adj
## Barbuda-Antigua 0.6045833 -7.475190  8.684356 0.9826131
## Bonaire-Antigua 8.7394246  2.249595 15.229255 0.0052116
## Bonaire-Barbuda 8.1348413  1.809338 14.460345 0.0080319

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  1.9666  0.146
##       88
##              Df Sum Sq Mean Sq F value   Pr(>F)    
## Island        2    813   406.7   12.46 1.26e-05 ***
## Residuals   115   3753    32.6                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 10 observations deleted due to missingness
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = for.bites ~ Island, data = vir20init, white.adjust = TRUE)
## 
## $Island
##                     diff        lwr      upr     p adj
## Barbuda-Antigua 3.431446  0.1293407 6.733552 0.0397136
## Bonaire-Antigua 5.966846  3.1227232 8.810969 0.0000067
## Bonaire-Barbuda 2.535400 -0.7532184 5.824018 0.1642219

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)   
## group   2  5.3717 0.005885 **
##       115                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4 Bivariate plots

4.1 Grazing as a function of fish size

Due to the lack of larger fish in Barbuda, these length-based relationships focus on comparisons between Antigua and Bonaire

4.2 Grazing impact as a function of scarid biomass

5 GAMMs

5.1 Scarus vetula

5.1.1 Feeding rates

vetinit <- data %>% filter(Species.Code=="qup" & Phase=="i")
gamm<-gamm(FR~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=vetinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # only PC1 and PC2 are significant, length slightly, scar.BM is not
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## FR ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1242.07      41.11   30.21   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df      F  p-value    
## s(Length.cm) 4.437  4.437  3.206   0.0297 *  
## s(scar.BM)   1.402  1.402  0.834   0.2519    
## s(PC1)       1.000  1.000 30.719 1.06e-07 ***
## s(PC2)       3.821  3.821  7.012 3.74e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.443   
##   Scale est. = 3.0251e+05  n = 179
AIC(gamm$lme)
## [1] 2753.156
plot(gamm$gam,pages=1)

5.1.2 Fraction of time spent grazing

gamm<-gamm(g.frac~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=vetinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # PC1 and PC2 are most significant, length is significant, scar.BM is almost significant
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g.frac ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.40498    0.01236   32.78   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df      F  p-value    
## s(Length.cm) 5.198  5.198  5.199 0.000135 ***
## s(scar.BM)   1.452  1.452  2.121 0.074590 .  
## s(PC1)       1.000  1.000 34.635 1.91e-08 ***
## s(PC2)       4.283  4.283 10.104 9.79e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.487   
##   Scale est. = 0.027324  n = 179
plot(gamm$gam,pages=1)

5.1.3 Grazing intensity

gamm<-gamm(for.bites~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=vetinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # very low R2, only PC1 and scar.BM significant
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## for.bites ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  12.2414     0.6197   19.75   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df     F p-value  
## s(Length.cm)   1      1 0.051  0.8211  
## s(scar.BM)     1      1 4.089  0.0448 *
## s(PC1)         1      1 5.932  0.0159 *
## s(PC2)         1      1 0.483  0.4880  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.179   
##   Scale est. = 64.525    n = 168
plot(gamm$gam,pages=1)

5.2 Sparisoma viride

5.2.1 Feeding rates

virinit <- data %>% filter(Species.Code=="stop" & Phase=="i")
gamm<-gamm(FR~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=virinit, random=list(Island=~1),method="REML")
summary(gamm$gam) #PC1, length, and scar.BM are significant predictors
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## FR ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   466.37      17.92   26.03   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df      F  p-value    
## s(Length.cm) 1.00   1.00 15.856 9.35e-05 ***
## s(scar.BM)   1.00   1.00  4.696   0.0313 *  
## s(PC1)       3.12   3.12 17.807 1.22e-10 ***
## s(PC2)       1.00   1.00  1.796   0.1816    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.332   
##   Scale est. = 69343     n = 216
plot(gamm$gam,pages=1)

5.2.2 Fraction of time spent grazing

gamm<-gamm(g.frac~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=virinit, random=list(Island=~1),method="REML")
summary(gamm$gam) #PC1, length, and scar.BM are significant predictors
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g.frac ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.38137    0.01606   23.75   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df      F  p-value    
## s(Length.cm) 1.000  1.000  8.185  0.00464 ** 
## s(scar.BM)   1.000  1.000  5.765  0.01720 *  
## s(PC1)       3.216  3.216 18.017 6.86e-11 ***
## s(PC2)       1.000  1.000  1.581  0.21004    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.32   
##   Scale est. = 0.05571   n = 216
plot(gamm$gam,pages=1)

5.2.3 Grazing intensity

gamm<-gamm(for.bites~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=virinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # no significant predictors (scar.BM almost), low r2
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## for.bites ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    6.981      1.381   5.057 1.01e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df     F p-value  
## s(Length.cm) 1.00   1.00 2.301  0.1309  
## s(scar.BM)   1.00   1.00 0.011  0.9172  
## s(PC1)       2.56   2.56 2.936  0.0743 .
## s(PC2)       1.00   1.00 1.242  0.2665  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.151   
##   Scale est. = 32.194    n = 194
plot(gamm$gam,pages=1)